Related papers: Gravitational instability of expanding shells: Sol…
We investigate mathematical properties of the system of nonlinear partial differential equations that describe, under certain simplifying assumptions, evolutionary processes in water-saturated granular materials. The unconsolidated solid…
We investigate spherically symmetric gravitational collapse of thick matter shell without radiation in the Einstein gravity with cosmological constant. The orbit of the infalling thick matter is determined by imposing an equation of state…
We present the results of smoothed particle hydrodynamic simulations investigating the evolution and fragmentation of filaments that are accreting from a turbulent medium. We show that the presence of turbulence, and the resulting…
We subject the stationary solutions of inviscid and axially symmetric rotational accretion to a time-dependent radial perturbation, which includes nonlinearity to any arbitrary order. Regardless of the order of nonlinearity, the equation of…
Simple strain-rate viscoelasticity models of isotropic soft solid are introduced. The constitutive equations account for finite strain, incompressibility, material frame-indifference, nonlinear elasticity, and viscous dissipation. A…
A freely falling stream of weakly cohesive granular particles is modeled and analysed with help of event driven simulations and continuum hydrodynamics. The former show a breakup of the stream into droplets, whose size is measured as a…
In nonlinear dynamical systems with highly nonorthogonal linear eigenvectors, linear non-modal analysis is more useful than normal mode analysis in predicting turbulent properties. However, the non-trivial time evolution of non-modal…
The roughening of expanding flame fronts by the accretion of cusp-like singularities is a fascinating example of the interplay between instability, noise and nonlinear dynamics that is reminiscent of self-fractalization in Laplacian growth…
In a recent one-dimensional numerical fluid simulation study [Saxena et al., Phys. Plasmas 13,032309 (2006)], it was found that an instability is associated with a special class of one-dimensional nonlinear solutions for modulated light…
The properties of pulse propagation in a nonlinear fiber including linear damped term added in the usual nonlinear Schr\"odinger equation is analyzed analytically. We apply variational modified approach based on the lagrangian that describe…
The gravitational clustering of collisionless particles in an expanding universe is modelled using some simple physical ideas. I show that it is possible to understand the nonlinear clustering in terms of three well defined regimes: (1)…
A model of nonlinear elastic medium with internal structure is considered. The medium is assumed to contain cavities, microcracks or blotches of substances that differ sharply in physical properties from the base material. To describe the…
We examine the general question of statistical changes experienced by ensembles of nonlinear random waves propagating in systems ruled by integrable equations. In our study that enters within the framework of integrable turbulence, we…
An outstanding problem in Earth science is understanding the method of transport of magma in the Earth's mantle. Models for this process, transport in a viscously deformable porous media, give rise to scalar degenerate, dispersive,…
The linear response of an isolated, homogeneous granular fluid to small spatial perturbations is studied by methods of non-equilibrium statistical mechanics. The long wavelength linear hydrodynamic equations are obtained, with formally…
We investigate the evolution equation of linear density perturbations in the Friedmann-Robertson-Walker universe with matter, radiation and the cosmological constant. The concept of solvability by quadratures is defined and used to prove…
The two-dimensional cubic nonlinear Schrodinger equation (NLS) can be used as a model of phenomena in physical systems ranging from waves on deep water to pulses in optical fibers. In this paper, we establish that every one-dimensional…
Inhomogeneous plasmas filaments instabilities are investigated by using the techniques of classical differential geometry of curves where Frenet torsion and curvature describe completely the motion of curves. In our case the Frenet frame…
We introduce three models of fragmentation in which the largest fragment in the system can be broken at each time step with a fixed probability, p. We solve these models exactly in the long time limit to reveal stable time invariant…
We present a theoretical and experimental study of the fragmentation of closed thin shells made of a disordered brittle material. Experiments were performed on brown and white hen egg-shells under two different loading conditions: impact…